What is 3ln(x^3e^{x^4}) ?

The solution to 3ln(x^3e^{x^4}) is 9ln(x)+3x^4

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simplify 3ln(x^3e^{x^4})

simplify

3 ln (x^{3} e^{x^{4}})

9 ln (x) + 3 x^{4}

Solution steps

3 ln (x^{3} e^{x^{4}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

3 ln (x^{3} e^{x^{4}}) = 3 ln (x^{3}) + 3 ln (e^{x^{4}})

= 3 ln (x^{3}) + 3 ln (e^{x^{4}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{3}) = 3 ln (x)

= 3 \cdot 3 ln (x) + 3 ln (e^{x^{4}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{x^{4}}) = x^{4} ln (e)

= 3 \cdot 3 ln (x) + 3 x^{4} ln (e)

3 \cdot 3 ln (x) = 9 ln (x)

3 x^{4} ln (e) = 3 x^{4}

= 9 ln (x) + 3 x^{4}

ln (\frac{tan ^{2} ( x )}{e ^{7 x^{4}} x ^{6}})

6 ln (3 x)

ln (L \cdot 0.47)

10 lo g_{10} (\frac{( 2.5 ) ^{2}}{1000}) + 40 + 59

\frac{1}{0.025} \cdot ln (\frac{100}{2})